document.write( "Question 860872: find two positive integers that differ by 8 and whose reciprocal differ by 1/6. \r
\n" ); document.write( "\n" ); document.write( "I would really appreciate it if yall could help me with this question!!! Thank you soo much for taking your time to help me too:) god bless
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Algebra.Com's Answer #518679 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the integers be $\"+a+\"$ and $\"+b+\"$
\n" ); document.write( "Assume that $\"+a+\"$ is the larger
\n" ); document.write( "(1) $\"+a+-+b+=+8+\"$
\n" ); document.write( "(2) $\"+1%2Fb+-+1%2Fa+=+1%2F6+\"$
\n" ); document.write( "Note that 1 / ( small number) is greater than 1 / ( big number )
\n" ); document.write( "-----------------------
\n" ); document.write( "(2) $\"+1%2Fb+-+1%2Fa+=+1%2F6+\"$
\n" ); document.write( "Multiply both sides by $\"+6%2Aa%2Ab+\"$
\n" ); document.write( "(2) $\"+6a+-+6b+=+a%2Ab+\"$
\n" ); document.write( "(2) $\"+6a+-+a%2Ab+=+6b+\"$
\n" ); document.write( "(2) $\"+a%2A%28+6+-+b+%29+=+6b+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+=+8+%2B+b+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( "(2) $\"+%28+8+%2B+b+%29%2A%28+6+-+b+%29+=+6b+\"$
\n" ); document.write( "(2) $\"+48+%2B+6b+-+8b+-+b%5E2+=+6b+\"$
\n" ); document.write( "(2) $\"+-b%5E2+-+2b+-+48+=+6b+\"$
\n" ); document.write( "(2) $\"+b%5E2+%2B+8b+-+48+=+0+\"$
\n" ); document.write( "(2) $\"+%28+b+%2B+12+%29%2A%28+b+-+4+%29+=+0+\"$
\n" ); document.write( " $\"+b+=+4+\"$ ( choose the positive root )
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+=+8+%2B+b+\"$
\n" ); document.write( "(1) $\"+a+=+8+%2B+4+\"$
\n" ); document.write( "(1) $\"+a+=+12+\"$
\n" ); document.write( "The integers are 4 and 12
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+1%2Fb+-+1%2Fa+=+1%2F6+\"$
\n" ); document.write( "(2) $\"+1%2F4+-+1%2F12+=+1%2F6+\"$
\n" ); document.write( "(2) $\"+3%2F12+-+1%2F12+=+2%2F12+\"$
\n" ); document.write( "(2) $\"+2%2F12+=+2%2F12+\"$
\n" ); document.write( "OK\r
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